# Revisiting the light cone of the Gödel universe

@article{Dautcourt2005RevisitingTL, title={Revisiting the light cone of the G{\"o}del universe}, author={Georg Dautcourt and M. Abdel-Megied}, journal={Classical and Quantum Gravity}, year={2005}, volume={23}, pages={1269 - 1288} }

The structure of a light cone in the Gödel universe is studied. We derive the intrinsic cone metric, calculate the rotation coefficients of the ray congruence forming the cone, determine local differential invariants up to second order, describe the crossover (keel) singularities and give a first discussion of its focal points. Contrary to many rotation coefficients, some inner differential invariants attain simple finite standard values at focal singularities.

## 7 Citations

### The lightcone of Gödel-like spacetimes

- Physics, Mathematics
- 2010

A study of the lightcone of the Gödel universe is extended to the so-called Gödel-like spacetimes. This family of highly symmetric 4D Lorentzian spaces is defined by metrics of the form , together…

### THE LIGHT CONE OF THE ANTI MACH SPACE-TIME

- Physics, MathematicsAssiut University Journal of Multidisciplinary Scientific Research
- 2015

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### Application of Lagrange Mechanics for Analysis of the Light-Like Particle Motion in Pseudo-Riemann Space

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- 2012

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### On the Riemann extension of the Godel space-time metric

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- 2005

Some properties of the Godel space-metric and its Riemann extension are studied. The spectrum of de Rham operator acting on 1-forms is studied. The examples of translation surfaces of the Godel…

### Curvature properties of Gödel metric

- MathematicsInternational Journal of Geometric Methods in Modern Physics
- 2019

The main aim of this paper is to investigate the geometric structures admitting by the Gödel spacetime which produces a new class of semi-Riemannian manifolds. We also consider some extension of…

### On the Matter of Time

- Art
- 2015

Abstract Drawing on several disciplinary areas, this article considers diverse cultural concepts of time, space, and materiality. It explores historical shifts in ideas about time, observing that…

### Building a Modern Myth

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- 2015

Building a Modern Myth is a multi-layered web endeavor that combines narrative filmmaking, documentary, social media, analytic philosophy, and theoretical physics into a creative exploration of how…

## References

SHOWING 1-10 OF 40 REFERENCES

### Approaches to Gödel's rotating universe

- Physics
- 2001

It is shown that the Newtonian analogue of Godel's rotating universe can be understood as the limit of a stellar model with negative cosmological constant in a quadrupole field. The essential part of…

### Characteristic Hypersurfaces in General Relativity. I

- Mathematics
- 1967

Lightlike (null) hypersurfaces are treated by means of an intrinsic Ricci rotation coefficient technique. This provides an effective way of dealing with the various types of geometry on a null…

### A Remarkable Property of Plane Waves in General Relativity

- Mathematics
- 1965

The complete general-relativistic plane-wave space-times (gravitational, electromagnetic, or both) are examined in relation to the focusing effect they exert on null cones. The following remarkable…

### The behavior of null geodesics in a class of rotating space-time homogeneous cosmologies

- Physics, Mathematics
- 1981

The null geodesics are investigated in a class of open space-time homogeneous cosmological models with rotating sheared matter (Ozsváth classIII). Gödel's model is a special case. A stationary polar…

### Dynamics and stability of the Godel universe

- Physics
- 2003

We use covariant techniques to describe the properties of the Godel universe and then consider its linear response to a variety of perturbations. Against matter aggregations, we find that the…

### Characteristic initial data and wavefront singularities in general relativity

- Physics, MathematicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1983

The structure of singularities (caustics), self-intersections of wavefronts (null hypersurfaces) and wavefront families (null coordinates) in arbitrary space-times is discussed in detail and…

### Gravitational Lensing from a Spacetime Perspective

- PhysicsLiving reviews in relativity
- 2004

The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations, and includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images.

### Exact Models of Charged Black Holes I. Geometry of Totally Geodesic Null Hypersurface*

- Mathematics
- 2004

. Inner geometry and embedding formulas for a totally geodesic null hyper- surface Ji in an electrovacuum space-time are given. The structure of all possible symmetry groups of the geometry is…

### Gödel’s trip

- Physics
- 2003

We discuss the geometrical light cone structure in Godel’s rigidly rotating cosmos and correct a picture in the standard literature.

### Dust‐Filled Universes of Class II and Class III

- Mathematics, Physics
- 1970

I construct on the Lie group R × H3 two different families of left‐invariant metrics which satisfy the Einstein field equations with incoherent matter, calling the Riemannian spaces M4, obtained this…